# Need some help with an exponent simplification questions

1. Apr 11, 2007

### i-love-physics

1. The problem statement, all variables and given/known data

express the given expression in simplest form with only possitive exponents

2. Relevant equations

**refer to attached drawing**

3. The attempt at a solution

Refer to attached drawing to see my attempt and to see what the real answer is. I dont understand where i went wrong in my steps, in the final answer there is a (-4n) i dont know where that came from.

Greatly appreciated if one of you smart guys could lend us a hand. Thank you.

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2. Apr 11, 2007

### HallsofIvy

you have
$$\left(\frac{1}{n}- \frac{2}{n}\right)^2$$
and say that is equal to
$$\left(\frac{n-2n^2}{n^3}\right)^2$$
While they are equal, the LEAST common denominator is n2, not n3. You do, in fact, eventually cancel the spare "n"s so that is not the problem.

The real problem is that you have
$$\left(\frac{n- 2n^2}{n^3}\right)^2$$
and say that is equal to
$$\frac{n^2- 4n^4}{n^6}$$
That is incorrect: (a- b)2 is NOT a2- b2!
It is a2- 2ab+ b2. You forgot the "middle term".

3. Apr 11, 2007

### i-love-physics

thanks

Thanks alot HallsofIvy, i appreciate your help mate.

It was such an obvious solution i cant believe i didnt figure it out myself.

Why does this happen sometimes?, the answer is right in front of you but a person still fails to see it?

I think i must be tired from work that is why. Or mybe i am craming in too much maths information into my brain in such a short period of time.

Anyway...thanks again.